pdf (it, 2.898,97 KB, 25/01/13)

P1 P2 P3
√
1 3
df(−1, 0) = − dx, df , ±
2 2
= 1
√
3
dx ±
2 2 dy.
P1 r1 : x = q1 q1
P1 x = −1
P2 1
P2 r2 : 1
2 x +
2 x+
√
3
√ 3
2
P3 1
P3 r3 : 1
2
x −
2 y = q2 q2
y = 1
2 x−
y = 1
√ 3
2
√ 3
2 y = q3 q3
r2 ∩ r3 = {(2, 0)} r1 ∩ r2 = {(−1, √ 3)} r1 ∩ r2 = {(−1, − √ 3)}
√ 12 = 2 √ 3
∂yf(P1) = 0
Γ ∂yf(P2) = − √ 3/2 = 0 ∂yf(P3) =
√ 3/2 = 0
y = ϕ2(x) y = ϕ3(x) x = 1/2 C 1 ϕ2(1/2) = √ 3/2
ϕ3(1/2) = − √ 3/2 ϕ2 ϕ3 1/2
ϕ ′ 2 (1/2) = −√ 3/3 ϕ ′ 3 (1/2) = √ 3/3
ρ 2 ρ = − cos 3θ
w(θ) = cos 2 (3θ) w
w ′ (θ) = −6 cos(3θ) sin(3θ) = −3 sin(6θ)
w ′′ (θ) = 18 cos(6θ)
θ = kπ/6 k = 0, 1, ..., 5
k = 2, 3, 4 k = 0, 1, 5
k = 0, 1, 5 Γ ρ = 0
(0, 0) ρ 2 = 0 k = 2, 3, 4
(−1, 0) (1/2, √ 3/2) (1/2, − √ 3/2)
ρ 2 1
f ρ ≤ 1 Γ
Γ
Γ
1 1 P1 P2 P3
Γ \ {(0, 0)}
∂yf(x, y) = 0 f(x, y) = 0 y = 0 y 2 =
(3x − 2x 2 )/2 x = 0 x = −1 x 2 (16x − 9)/4 =
0 x = 9/16 y = ±3 √ 15/16
P1 = Q1 = (−1, 0), Q2 =
9
16 , 3√
15
9
, Q3 =
16
16 , −3√
15
,
16
Q3 x Q2 Γ
q(x, y) = x Γ
∇f ∇q Γ
∇f = (0, 0)
q(Q1) < q(0, 0) = 0 < q(Q2) = q(Q3) Q1